Aim

To estimate the percentage of symptomatic COVID-19 cases reported in different countries using case fatality ratio estimates based on data from the ECDC, correcting for delays between confirmation-and-death.

Methods Summary

In real-time, dividing deaths-to-date by cases-to-date leads to a biased estimate of the case fatality ratio (CFR), because this calculation does not account for delays from confirmation of a case to death, and under-reporting of cases.
Using the distribution of the delay from hospitalisation-to-death for cases that are fatal, we can estimate how many cases so far are expected to have known outcomes (i.e. death or recovery), and hence adjust the naive estimates of CFR to account for these delays.
The adjusted CFR does not account for under-reporting. However, the best available estimates of CFR (adjusting or controlling for under-reporting) are in the 1% - 1.5% range [1–4]. Large studies in China and South Korea estimating the CFR at 1.38% (95% CrI: 1.23–1.53%)[2] and 1.4% (95% CrI: 1.2-1.7%)[4] respectively. Based on these studies, and for simplicity, we assume a baseline CFR of 1.4% for our analysis.
If a country has an adjusted CFR that is higher (e.g. 20%), it suggests that only a fraction of cases have been reported (in this case, 1.420=7.0% cases reported approximately).

Current estimates for percentage of symptomatic cases reported for countries with greater than ten deaths

Temporal variation

Figure 1: Temporal variation in reporting rate. We calculate the percentage of symptomatic cases reported on each day a country has had more than ten deaths. We then fit a Gaussian Process (GP) to these data (see Temporal variation model fitting section for details), highlighting the temporal trend of each countries reporting rate. The red shaded region is the 95% CrI of fitted GP.

Adjusted symptomatic case estimates

Figure 2: Estimated number of new symptomatic cases, calculated using our temporal under-reporting estimates. We adjust the reported case numbers each day - for each country with an under-reporting estimate - using our temporal under-reporting estimates to arrive at an estimate of the true number of symptomatic cases each day. The shaded blue region represents the 95% CrI, calcuated directly using the 95% CrI of the temporal under-reporting estimate.

Reported cases

Figure 3: Reported number of cases each day, pulled from the ECDC and plotted against time for comparison with our estimated true numbers of symptomatic cases each day, adjusted using our under-reporting estimates.

Table of current estimates

Country	Percentage of symptomatic cases reported (95% CI)	Total cases	Total deaths
Afghanistan	59% (43%-79%)	26,874	504
Albania	89% (49%-100%)	1,722	38
Algeria	20% (14%-28%)	11,268	799
Andorra	37% (18%-82%)	854	52
Argentina	52% (40%-65%)	35,539	913
Armenia	55% (42%-69%)	18,033	302
Australia	91% (67%-100%)	7,370	102
Austria	84% (43%-100%)	17,115	687
Azerbaijan	82% (61%-100%)	10,991	133
Bahrain	97% (87%-100%)	19,961	49
Bangladesh	85% (68%-100%)	98,489	1,305
Belarus	99% (87%-100%)	56,032	324
Belgium	38% (25%-52%)	60,244	9,675
Bolivia	34% (26%-42%)	20,685	679
Bosnia and Herzegovina	59% (26%-96%)	3,141	168
Brazil	37% (30%-44%)	955,377	46,510
Bulgaria	22% (16%-31%)	3,542	184
Burkina Faso	59% (26%-97%)	899	53
Cameroon	32% (22%-46%)	9,864	276
Canada	25% (20%-30%)	99,842	8,254
Chad	60% (21%-96%)	854	74
Chile	59% (52%-66%)	220,628	3,615
China	38% (16%-67%)	84,458	4,638
Colombia	28% (22%-34%)	57,046	1,864
Congo	43% (23%-75%)	883	27
Costa Rica	89% (62%-100%)	1,871	12
Cote dIvoire	93% (75%-100%)	6,063	48
Croatia	21% (8.5%-41%)	2,258	107
Cuba	82% (49%-100%)	2,280	84
Cyprus	84% (46%-100%)	985	18
Czechia	76% (48%-99%)	10,162	333
Democratic Republic of the Congo	61% (29%-92%)	5,099	115
Denmark	59% (36%-83%)	12,294	598
Djibouti	90% (68%-100%)	4,545	43
Dominican Republic	64% (37%-95%)	24,105	633
Ecuador	17% (14%-21%)	48,490	4,007
Egypt	26% (21%-32%)	49,219	1,850
El Salvador	56% (39%-78%)	4,066	82
Equatorial Guinea	91% (67%-100%)	1,306	12
Estonia	43% (25%-76%)	1,977	69
Ethiopia	38% (27%-53%)	3,759	63
Finland	81% (48%-100%)	7,117	326
France	46% (36%-54%)	158,174	29,575
Gabon	95% (78%-100%)	4,229	30
Georgia	77% (40%-100%)	893	14
Germany	47% (36%-60%)	187,764	8,856
Ghana	98% (88%-100%)	12,590	66
Greece	26% (16%-41%)	3,203	187
Guatemala	29% (21%-39%)	11,251	432
Guinea	96% (83%-100%)	4,668	26
Guinea Bissau	58% (25%-98%)	1,492	15
Guyana	55% (17%-99%)	171	12
Haiti	83% (52%-100%)	4,688	82
Honduras	38% (27%-51%)	10,299	336
Hungary	13% (8.4%-18%)	4,079	568
Iceland	86% (48%-100%)	1,815	10
India	33% (27%-39%)	366,946	12,237
Indonesia	22% (17%-27%)	41,431	2,276
Iran	38% (31%-46%)	195,051	9,185
Iraq	23% (18%-29%)	24,254	773
Ireland	26% (17%-40%)	25,341	1,710
Israel	85% (66%-99%)	19,894	303
Italy	12% (9.6%-14%)	237,828	34,448
Jamaica	64% (19%-100%)	626	10
Japan	44% (28%-63%)	17,668	935
Jersey	20% (7.3%-58%)	318	30
Kazakhstan	95% (62%-100%)	15,877	100
Kenya	52% (34%-75%)	4,044	107
Kosovo	72% (41%-100%)	1,486	33
Kuwait	97% (89%-100%)	37,533	306
Kyrgyzstan	85% (57%-100%)	2,657	31
Latvia	40% (17%-72%)	1,104	30
Lebanon	78% (43%-100%)	1,489	32
Liberia	27% (12%-60%)	509	33
Lithuania	28% (14%-44%)	1,778	76
Luxembourg	56% (36%-84%)	4,085	110
Malaysia	96% (73%-100%)	8,515	121
Mali	23% (16%-35%)	1,890	107
Mauritania	14% (9.9%-19%)	2,057	93
Mexico	12% (9.7%-14%)	159,793	19,080
Moldova	33% (25%-41%)	12,732	433
Morocco	97% (79%-100%)	8,997	213
Nepal	96% (85%-100%)	7,177	20
Netherlands	48% (34%-65%)	49,204	6,074
Nicaragua	93% (59%-100%)	2,014	64
Niger	31% (13%-76%)	1,020	67
Nigeria	54% (41%-70%)	17,735	469
North Macedonia	22% (16%-29%)	4,482	210
Norway	81% (41%-100%)	8,660	243
Oman	98% (90%-100%)	26,079	116
Pakistan	57% (46%-68%)	160,118	3,093
Panama	73% (45%-100%)	22,597	470
Paraguay	93% (71%-100%)	1,308	13
Peru	35% (28%-42%)	240,908	7,257
Philippines	70% (52%-88%)	27,238	1,108
Poland	47% (35%-60%)	30,701	1,286
Portugal	62% (45%-80%)	37,672	1,523
Puerto Rico	93% (77%-100%)	6,003	147
Qatar	87% (40%-100%)	83,174	82
Romania	20% (14%-28%)	22,760	1,451
Russia	68% (57%-79%)	553,301	7,478
San Marino	84% (32%-100%)	696	42
Sao Tome and Principe	83% (49%-100%)	683	12
Saudi Arabia	51% (41%-63%)	141,234	1,091
Senegal	85% (61%-100%)	5,369	73
Serbia	94% (69%-100%)	12,522	257
Sierra Leone	72% (40%-99%)	1,249	51
Singapore	88% (50%-100%)	41,216	26
Slovakia	75% (43%-100%)	1,561	28
Slovenia	21% (11%-44%)	1,513	109
Somalia	70% (42%-96%)	2,696	88
South Africa	39% (31%-46%)	80,412	1,674
South Korea	82% (52%-100%)	12,257	280
South Sudan	59% (32%-93%)	1,807	31
Sri Lanka	93% (74%-100%)	1,924	11
Sudan	20% (14%-28%)	8,020	487
Sweden	50% (40%-60%)	54,562	5,041
Switzerland	35% (24%-50%)	31,100	1,677
Tajikistan	99% (89%-100%)	5,221	51
Thailand	79% (48%-100%)	3,141	58
Togo	83% (50%-100%)	544	13
Tunisia	54% (20%-99%)	1,128	50
Turkey	85% (69%-97%)	182,727	4,861
Ukraine	48% (35%-63%)	33,234	943
United Arab Emirates	98% (85%-100%)	43,364	295
United Kingdom	19% (15%-22%)	299,251	42,153
United Republic of Tanzania	60% (28%-98%)	509	21
United States of America	45% (37%-53%)	2,163,290	117,717
Uruguay	55% (27%-96%)	849	24
Uzbekistan	97% (85%-100%)	5,697	19
Venezuela	94% (76%-100%)	3,150	27
Yemen	1.1% (0.78%-1.6%)	902	244

Table 1: Estimates for the proportion of symptomatic cases reported in different countries using cCFR estimates based on case and death timeseries data from the ECDC. Total cases and deaths in each country is also shown. Confidence intervals calculated using an exact binomial test with 95% significance.

Adjusting for outcome delay in CFR estimates

During an outbreak, the naive CFR (nCFR), i.e. the ratio of reported deaths date to reported cases to date, will underestimate the true CFR because the outcome (recovery or death) is not known for all cases [5]. We can therefore estimate the true denominator for the CFR (i.e. the number of cases with known outcomes) by accounting for the delay from confirmation-to-death [1].

We assumed the delay from confirmation-to-death followed the same distribution as estimated hospitalisation-to-death, based on data from the COVID-19 outbreak in Wuhan, China, between the 17th December 2019 and the 22th January 2020, accounting right-censoring in the data as a result of as-yet-unknown disease outcomes (Figure 1, panels A and B in [7]). The distribution used is a Lognormal fit, has a mean delay of 13 days and a standard deviation of 12.7 days [7].

To correct the CFR, we use the case and death incidence data to estimate the proportion of cases with known outcomes [1,6]:

\[ u_{t} = \frac{ \sum_{j = 0}^{t} c_{t-j} f_j}{c_t}, \]

where \(u_t\) represents the underestimation of the proportion of cases with known outcomes [1,5,6] and is used to scale the value of the cumulative number of cases in the denominator in the calculation of the cCFR, \(c_{t}\) is the daily case incidence at time, \(t\) and \(f_t\) is the proportion of cases with delay of \(t\) between confirmation and death.

Approximating the proportion of symptomatic cases reported

At this stage, raw estimates of the CFR of COVID-19 correcting for delay to outcome, but not under-reporting, have been calculated. These estimates range between 1% and 1.5% [1–3]. We assume a CFR of 1.4% (95% CrI: 1.2-1.7%), taken from a recent large study [3], as a baseline CFR. We use it to approximate the potential level of under-reporting in each country. Specifically, we perform the calculation \(\frac{1.4\%}{\text{cCFR}}\) of each country to estimate an approximate fraction of cases reported.

Temporal variation model fitting

We estimate the level of under-reporting on every day for each country that has had more than ten deaths. We then fit a Gaussian Process (GP) model using the library greta and greta.gp. The parameters we fit and their priors are the following: \[ \begin{aligned} &\sigma \sim \text{Log Normal(-1, 1)}: \quad &\text{Variance of the reporting kernel} \\ &\text{L} \sim \text{Log Normal(4, 0.5)}: \quad &\text{Lengthscale of the reporting kernel} \\ &\sigma_{\text{obs}} \sim \text{Truncated Normal(0, 0.5)}, \quad &\text{Variance of the obseration kernel, truncated at 0} \end{aligned} \] The kernel is split into two components: the reporting kernel \(R\), and the observation kernel \(O\). The reporting component has a standard squared-exponential form. For the observation component, we use an i.i.d. noise kernel to acccount for observation overdispersion, which can smooth out overly clumped death time-series. This is important as some countries have been known to report an unusually large number of deaths on a single day, due to past under-reporting.

In the sampling and fitting process, we calculate the expected number of deaths at each time-point, given the baseline CFR. We then use a Poisson likelihood, where the expected number of deaths is the rate of the Poisson likelihood, given the observed number of deaths

Adjusting case counts for under-reporting

We adjust the reported number of cases each day, pulled from the ECDC. Specifically, we divide the case numbers of each day by our “proportion of cases reported” estimates that we calculate each day for each country.*

Limitations

Implicit in assuming that the under-reporting is \(\frac{1.4\%}{\text{cCFR}}\) for a given country is that the deviation away from the assumed 1.4% CFR is entirely down to under-reporting. In reality, burden on healthcare system is a likely contributing factor to higher than 1.4% CFR estimates, along with many other country specific factors.

The following is a list of the other prominent assumptions made in our analysis:

We assume that people get tested upon hospitalisation. A few examples where this is not the case are Germany and South Korea, where people can get tested earlier.
We assume that hospitalisation to death from early Wuhan is representative of the all the other countries (by using the distribution parameterised using early Wuhan data) and that all countries have the same risk and age profile as Wuhan.
Severity of COVID-19 is known to increase with age. Therefore, countries with older populations will naturally see higher death rates. We are extending this analysis to adjust for the age distribution for countries with more than five reported deaths and where age distribution data is available.
All results are linked and biased by the baseline CFR, assumed at 1.4% [3].
The under-reporting estimate is sensitive to the baseline CFR, meaning that small errors in it lead to large errors in the estimate for under-reporting.
There are several sources of uncertainty in this analysis: the reported mean and SD of the delay distribution; the cCFR for each country (on each day) and the baseline CFR. We use the lower and upper mean and SD of the delay distribution to produce the widest interval. The other two uncertainties are just carried through directly in the subsequent calculations, which is crude. An ongoing extension is developing this into a fully Bayesian model, which deals with these different uncertainties more rigorously.

Code and data availability

The code is publically available at https://github.com/thimotei/CFR_calculation. The data required for this analysis is a time-series for both cases and deaths, along with the corresponding delay distribution. We scrape this data from ECDC, using the NCoVUtils package [8].

Acknowledgements

The authors, on behalf of the Centre for the Mathematical Modelling of Infectious Diseases (CMMID) COVID-19 working group, wish to thank DSTL for providing the High Performance Computing facilities and associated expertise that has enabled these models to be prepared, run and processed and in an appropriately-rapid and highly efficient manner.

References

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2 Verity R, Okell LC, Dorigatti I et al. Estimates of the severity of covid-19 disease. medRxiv 2020.

3 Guan W-j, Ni Z-y, Hu Y et al. Clinical characteristics of coronavirus disease 2019 in china. New England Journal of Medicine 2020.

4 Shim E, Mizumoto K, Choi W et al. Estimating the risk of covid-19 death during the course of the outbreak in korea, february-march, 2020. medRxiv 2020.

5 Kucharski AJ, Edmunds WJ. Case fatality rate for ebola virus disease in west africa. The Lancet 2014;384:1260.

6 Nishiura H, Klinkenberg D, Roberts M et al. Early epidemiological assessment of the virulence of emerging infectious diseases: A case study of an influenza pandemic. PLoS One 2009;4.

7 Linton NM, Kobayashi T, Yang Y et al. Incubation period and other epidemiological characteristics of 2019 novel coronavirus infections with right truncation: A statistical analysis of publicly available case data. Journal of Clinical Medicine 2020;9:538.

8 Abbott S MJ Hellewell J. NCoVUtils: Utility functions for the 2019-ncov outbreak. doi:105281/zenodo3635417 2020.